We report the structural and magnetic properties of a new system LiRhMnO$_{4}$ (LRMO) through x-ray diffraction, bulk magnetization, heat capacity and $^{7}$Li nuclear magnetic resonance (NMR) measurements. LRMO crystallizes in the cubic space group $mathit{Fd}$$bar{3}$$mathit{m}$. From the DC susceptibility data, we obtained the Curie-Weiss temperature $mathrm{theta}_{mathrm{CW}}$ = -26 K and Curie constant $mathit{C}$ = 1.79 Kcm$^{3}$/mol suggesting antiferromagnetic correlations among the magnetic Mn$^{4+}$ ions with an effective spin $mathit{S}$ = $frac{3}{2}$. At $mathit{H}$ = 50 Oe, the field cooled and zero-field cooled magnetizations bifurcate at a freezing temperature, $T_{f}$ = 4.45 K, which yields the frustration parameter $mathit{f=frac{midtheta_{CW}mid}{T_{f}}}>$5. AC susceptibility, shows a cusp-like peak at around $T_{f}$, with the peak position shifting as a function of the driving frequency, confirming a spin-glass-like transition in LRMO. LRMO also shows typical spin-glass characteristics such as memory effect, aging effect and relaxation. In the heat capacity, there is no sharp anomaly down to 2 K indicative of long-range ordering. The field sweep $^{7}$Li NMR spectra show broadening with decreasing temperature without any spectral line shift. The $^{7}$Li NMR spin-lattice and spin-spin relaxation rates also show anomalies due to spin freezing near $T_{f}$.
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